In this paper, we study games where we have probabilistic information about the vNM functions of players. For example, in school choice, it might be clear that a student prefers one school much more than another, but it is not exactly clear by how much. We model this probabilistic information about the vNM functions of opponents via types in a Bayesian game. However, we do not search for a Bayes-Nash equilibrium in these games, which share the same problems as standard Nash equilibrium: there can be many equilibria, and finding equilibrium is PPAD-hard [1]}.
Instead, we follow a novel approach that is fundamentally different from the NE's normative one: Markov-Conley-Chains (MCCs) and the \(\alpha \) -Rank algorithm, which were recently proposed for normal-form games [2]}.
